Management Accounting Math

Problem: A large size company is considering to invest in a new project that costs Tk.4,00,000. The estimated salvage value is zero; tax rate is 35%. The company uses straight line depreciation and the proposed project has cash flows before tax (CBFT) as below: 

Year	Profit before Tax and Depreciation
1st year	1,00,000
2nd year	1,00,000
3rd year	1,50,000
4th year	1,50,000
5th year	2,50,000

Required: Determine the following: (i) Payback period; (ii) ARR; (iii) NPV at 15%; (iv) Profitability Index.

(The PV at 15% are 0.870; 0.756; 0.658; 0.572; 0.497)

Solution:

Depreciation = Cost – Salvage value/No. of year in lifetime = 4,00,000-0/5 = 80,000.

Statement of cash inflow:

Particulars	1st year	2nd year	3rd year	4th year	5th year
Profit before Tax & Depreciation Less Depreciation	1,00,000 80,000	1,00,000 80,000	1,50,000 80,000	1,50,000 80,000	2,50,000 80,000
Profit before Tax Less Tax @35%	20,000 7,000	20,000 7,000	70,000 24,500	70,000 24,500	1,70,000 59,500
Profit after Tax Add depreciation	13,000 80,000	13,000 80,000	45,500 80,000	45,500 80,000	1,10,500 80,000
Cash inflow	93,000	93,000	1,25,500	1,25,500	1,90,500

Required 1: (Pay Back Period (PBP):

Year	Cash inflow	Cumulative cash inflow
1	93,000	93,000
2	93,000	1,86,000
3	1,25,500	3,11,500
4	1,25,500	4,37,000
5	1,90,500	6,27,500

PBP = 3 + (Total investment – 3^rd year cumulative cash inflow)/4^th year cash inflow

        = 4 + (4,00,000 – 3,11,500)/1,25,500 = 3.71 years

Required 2: Average rate of return:

ARR= (Average annual profit / Average investment)*100

        =[{(13,000+13,000+45,500+45,500+1,10,500)/5}/(4,00,000)/2]*100=(45,500/2,00,000)*100

        = 22.75%

Required 3: Net Present Value (NPV) calculation:

Year	Cash flow	Discount factor@10%	Present value
1	93,000	0.870	80,910
2	93,000	0.756	70,308
3	1,25,500	0.658	82,579
4	1,25,500	0.572	71,786
5	1,90,500	0.497	94,679
Present Value of cash Less, investment	=4,00,262 =(4,00,000)
Net Present Value (NPV)	262

Required 4: Calculation of Profitability Index (PI)

PI = PV of cash inflow/PV of investment cost

     = 4,00,262/4,00,000 = 1.000655

Ans:

i)                    Pay Back Period 3.71 years

ii)                  ARR = 22.75%

iii)                NPV = 262

iv)                PI = 1.000655

Comments: Out of 5 years project life, the investment will return within 3.71 years, ARR is 22.75% which is higher than cost of capital, PI is greater than 1 and NPV value negative, So the project is viable.